Between 600 and 800 nm, Silver reflects about 97%, and Aluminum about 86%.

If you assume a value of 90% reflectance, for simplicity, you need to reflect the light x times, where .9^x = 10^-4. According to Wolframalpha, that's about 87 reflections.

After reflecting 87 times, your image of the sun will be extremely fuzzy. This is not a good way to view the sun.

You could do it with fewer reflections by using a glossy black surface. The http://www.reuters.com/article/2008/01/15/us-nano-black-idUSN1555030620080115 [Links inactive - To make links active and clickable, login or click here to register] reflects about .1% of incident light. If you can polish it to a mirror finish, you might only need to reflect the light twice.

A better way to view the sun is to project the light from a telescope's eyepiece thru a window onto a viewing screen in a dark room. Or you can buy a https://www.google.com/#hl=en&q=solar+filter&bpcl=35466521&um=1&ie=UTF-8&tbo=u&tbm=shop&source=og&sa=N&tab=wf&ei=Qq2EUPakFc_iigLX04G4Bw&bav=on.2,or.r_gc.r_pw.r_qf.&fp=5f266fec9f7ad0eb&biw=864&bih=411 [Links inactive - To make links active and clickable, login or click here to register] to put over the front of your telescope.

You could do it with fewer reflections by using a glossy black surface. The http://www.reuters.com/article/2008/01/15/us-nano-black-idUSN1555030620080115 [Links inactive - To make links active and clickable, login or click here to register] reflects about .1% of incident light. If you can polish it to a mirror finish, you might only need to reflect the light twice.

I don't think you could polish a carbon nanotube forest & preserve the optical properties. However, you might do well with a homogenous forest wtih all nanotubes having the same height, direction, and diameter.

http://en.wikipedia.org/wiki/Super_black [Links inactive - To make links active and clickable, login or click here to register] might have better optical properties, but does not have equal absorption across the spectrum, and thus IR might be too bright.

The sun is rather small, so it's hard to get a good look at.If you project an image of it that's bigger than the lens you use then that image is less bright than the sunlight.Also, if you project the image onto, for example, a bit of paper then that will scatter the light in all directions so only a small fraction of it will reach your eyes.

So projecting the light with a telescope is a very good solution but Don't ever look through a telescope at the sun.

We are used to looking through the thin direction at a mirror, but if you look at the mirror from its side, it looks very dark green to black. This is due to the light being strongly absorbed by passing through the width of the mirror, with no reflections.

Compare this to optical fibers, which lose less than 25% of the light after passing through a kilometer.

But the safest way to observe the sun is to project an image onto paper, without your eye looking in the direction of the sun (even accidentally).

The problem with trying to get any good quality pictures of the sun is that you need a room where most of the ambient light can be excluded and the only light that comes in is via the telescope, I was able to get good pictures of the first transit of Venus by this method but could not record the second one due to having moved and having no suitable line of sight. I think for high quality pictures a Density 5.0 filter is the only answer.I think Evan-au is rather pessimistic about the loss in high grade fibre optic cables

Astronomical telescopes using a mirror (as invented by Isaac Newton) avoid light absorption through the glass by coating the mirror surface facing the light source, rather than coating the rear surface as is done for bathroom mirrors.

Being exposed to the atmosphere, astronomers have to clean off the reflective metal surface and recoat it at regular intervals.

You also need to ensure that visitors don't leave fingerprints on the mirror....